An argument I hear repeatedly is the light-speed limit only applies where spacetime is flat, so faster-than-light speed is possible where spacetime is curved. Thus special relativity does not apply to our expanding universe which is theoretically expanding faster than light beyond the cosmological horizon. Here's the problem: the universe's spacetime is flat. The cosmological constant is a very small number in curvature units. The WMAP has empirically confirmed this flatness. So why wouldn't special relativity apply--especially the light-speed limit?
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"Spatially flat" is not the same thing as "flat spacetime". Even if the geometry at any moment of cosmological time $t$ is plain old Euclidean space, the expansion and contraction of this space as time goes on leads to non-zero spacetime curvature.
By way of analogy: the surface of the Earth can be thought of as the union of a bunch of circular lines of latitude, from 90°N to 90°S. Mathematically, a circle has no intrinsic curvature.* Yet the individual circles (with no curvature) form a two-dimensional surface with curvature.
*It has extrinsic curvature when you draw it on a plane, but extrinsic curvature isn't what we're talking about when we talk about spacetime curvature.
Michael Seifert
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Special relativity do of course also apply to our expanding universe. The statement of special relativity is not that there can be no speed faster than the speed of light, but that no information can be transported at speeds faster than the speed of light. The expansion of space does not transport information, so there is no contradiction.
rfl
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